Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×D388 | C2 | semidirect |
| 3. #20260638 | C2 | semidirect |
| 4. #20260636 | C2 | semidirect |
| 5. #20260614 | C2 | semidirect |
| 6. #20260611 | C2 | semidirect |
| 7. #20260600 | C2 | semidirect |
| 8. #20260581 | C2 | semidirect |
| 9. C2×C4×D4×C97 | C2 | semidirect |
| 13. #15690806 | C4 | semidirect |
| 33. C2×D388 | C2×C4 | semidirect |
| 36. C2×C22⋊D97 | C2×C4 | semidirect |
| 47. C4×Dic97 | C2×C4 | semidirect |
| 51. C2×D4×C97 | C2×C4 | semidirect |
| 60. C42×C97 | D4 | semidirect |
| 124. C97 | #2328 | semidirect |
| 127. C2×C4×D4 | D97 | semidirect |
| 164. C2×D4 | C4×D97 | semidirect |
| 184. C42 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690806 | 2 |
| C2×C4×D388 | 2 |
| #20260638 | 2 |
| #20260636 | 2 |
| #20260614 | 2 |
| #20260611 | 2 |
| #20260600 | 2 |
| #20260581 | 2 |
| C2×C4×D4×C97 | 2 |
| #2328 | 97 |